# Tagged Questions

For questions about the quaternions: a noncommutative four dimensional division algebra over the real numbers.

2answers
194 views

### How to calculate the quaternion from/and axis angle having parent and target position (camera and its target)?

I want to calculate the orientation (quaternion) of the virtual 3d camera that is looking at some point in 3d space. The illustration: According to this explanation the quaternion be calculated ...
2answers
48 views

### Can I write an expression that enters the quaternion space without expressing the variables associated?

First of all, forgive my little knowledge on the subject. I can enter the complex space by just using an expression only having real numbers, for example: ...
2answers
66 views

### Quaternion Multiplication: What is the correct way of doing it?

I am not very familiar with quaternions, I was just doing a programming homework were I had to implement quaternions' arithmetic, however I got puzzled by the multiplication of 2 quaternions. Let's ...
0answers
82 views

### Slerp formula interpretation

I have a problem about spherical linear interpolation, or slerp for short. As linked, Wikipedia gives the following formula for an interpolation between quaternions ...
1answer
155 views

### How are Quaternions derived from Complex numbers or Real numbers?

I understand how complex numbers are derived from real numbers. Namely when you have a sqrt of a negative number you must have an answer of some kind, but this answer cannot be in the real number ...
1answer
40 views

### What is the perspective projection of a 3d point relative to a quarternion encoded camera?

I'm representing a camera on the cartesian space as a tuple of a 3d point (position) and a quarternion (rotation). I get the front, right and up vectors of the camera by applying the quaternion to the ...
6answers
5k views

1answer
60 views

### Dot product of of quaternion-rotated vectors

I'm reading http://people.csail.mit.edu/bkph/articles/Quaternions.pdf and it says "it is easy to show that the operation preserves dot-products." on the page 3. But how is it done? I tried to make a ...
1answer
235 views

### Why is '1' the multiplicative identity of complex numbers and quaternions?

I am not a mathematician. I studied electrical engineering. I encountered quaternions while trying to understand motion of mobile robots and how rotations are achieved. This question occurred to me ...
0answers
221 views

### Calculating two rotation angles from xyz coordinates for dummies

This post is a bit verbose so that others who come later may benefit from my thick headedness. I am attempting to construct a primitives composition and constructed solids geometry parser/processor ...
1answer
234 views

### Multiplication of a quaternion and a scalar to produce a vector?

I am looking at someone else's code, and in it they have a quaternion multiplied with a scalar in order to produce a vector. He used the boost library, and can't find exactly where they defined the ...
1answer
41 views

### Geometric significance of map, quaternions.

Let $u, v, w \in \mathbb{R}^3$ be a triple of vectors which form an orthonormal basis in $\mathbb{R}^3$ (with the standard orientation). Identify $u, v, w$ with quaternions in the $\mathbb{R}$-linear ...
2answers
96 views

### Clarify: “$S^0$, $S^1$ and $S^3$ are the only spheres which are also groups”

The zero, one, and three dimensional spheres $S^0$, $S^1$ and $S^3$ are in bijection with the sets $\{a\in \mathbb{K}:|a|=1\}$ for $\mathbb{K} = \mathbb{R}, \mathbb{C}, \mathbb{H}$ respectively. The ...
0answers
56 views

### Factoring quaternion into three parts

I am faced with a problem where I have a quaternion which represents rotation and three arbitrary axis about which I can make rotations, thus three unit vectors. What I would like to know is angles (...
1answer
48 views

### Hasse invariant of quaternions over $\mathbb{Q}_p$

I am trying to compute the Hasse invariant of the quaternion algebra over $\mathbb{Q}_p$. I denote this algebra by $H$, and I'm assuming $p\equiv 3\pmod{4}$. So, $\mathbb{Q}_p(i)$ is an unramified ...
1answer
74 views

### Why multiplying those 2 quaternions doesn't give the expected result?

Using a left-handed coordinate system, let Q = axisAngle({0,0,1}, 1/4*pi) * axisAngle({0,1,0}, 1/4*pi) be the quaternion representing the rotation "1/8 circle ...
1answer
99 views

### understanding quaternions - spatial rotations

I would like to know if my understanding about quaternions is correct please: lets say you have a vector in 3d space. You could rotate the x,y and-z frame on a fixed point so that it is parallel with ...
1answer
61 views

### quaternions - understanding a formula

Quaternions are new for me. I am trying to understand the following formula: What are: $\large{q^x}$ ? I don't think it is a power. $\large{q^t}$ ? just a transposition of the quaternion $q$? ...
1answer
60 views

### what represents this strange matrix [closed]

But I just encountered a very strange type of matrix. What is the name of this type of matrix? How can it be solved? The final result should be a $4\times 4$ matrix, but I only see $5$ elements on ...
0answers
81 views

### How do I get the rotation between two rotationmatrices?

I am stuck on a little rotation problem. The problem: I have 2 rotation matrices $A$ and $B$. $A$ and $B$ are relative to the coordinate system O. $A$ and $B$ are Quaternion rotation matrices. I am ...
1answer
129 views

### Eigenvalues of Group Elements and Quaternions

The quaternion algebra is given by $\mathbb{H}$ = $\{a+bi+cj+dk \mid a, b, c, d \in \mathbb{R}, i^2 = j^2 = k^2 = -1, ij = k = -ji\} := \{z_1+z_2j \mid z_1, z_2 \in \mathbb{C}\}.$ I consider the 3-...
1answer
38 views

### Question about Eigenvalues of group elements

The quaternion algebra is given by $\mathbb{H}$ = $\{a+bi+cj+dk \mid a, b, c, d \in \mathbb{R}, i^2 = j^2 = k^2 = -1, ij = k = -ji\} := \{z_1+z_2j \mid z_1, z_2 \in \mathbb{C}\}.$ I consider the 3-...